Question

a red ball has a mass of 250 g . a constant force pushes the red ball horizontally and launches it at a speed of 15 m/s . the same force pushes a green ball through the same distance, launching it at 25 m/s . part a what is the mass of the green ball?

Answer 1

Using the work-energy principle and assuming the same amount of work is done on both balls, the mass of the green ball is calculated to be 90 grams by equating the kinetic energy imparted to both balls.

Step-by-step explanation:

To find the mass of the green ball, we will assume that the same force acts on both balls through the same distance, which means the work done on each ball is the same. Since work is also the change in kinetic energy, we can equate the kinetic energy imparted to each ball to find the relationship between their masses and velocities.

The kinetic energy (KE) of an object is given by the formula:

KE = (1/2) m v^2

For the red ball:

KEred = (1/2) * massred * (velocityred)^2

KEred = (1/2) * 0.25 kg * (15 m/s)^2

KEred = (1/2) * 0.25 kg * 225 m2/s2

KEred = 28.125 J

For the green ball:

KEgreen = (1/2) * massgreen * (velocitygreen)^2

Since work done is the same:

KEred = KEgreen

28.125 J = (1/2) * massgreen * (25 m/s)^2

massgreen = 28.125 J / (1/2 * 625 m2/s2)

massgreen = 28.125 J / 312.5 J/kg

massgreen = 0.09 kg

massgreen = 90 g

Therefore, the mass of the green ball is 90 grams.